Qualitative theory of dynamical systems and applications in the study of physical and biological phenomena

• Grant number: 23/04880-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2023
• End date: November 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcelo Messias
• Grantee: Thayná Machado Catelan
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

Study of the Qualitative Theory of Ordinary Differential Equations and its applications in mathematical modeling and analysis of natural phenomena, especially those from Physics, Biology and Engineering. It is intended to study the main mathematical models, which will serve as a tool to fix knowledge and as a basis for the study of new proposed models that do not appear in the literature. The theoretical part will be studied and computational experiments will be carried out, with the aid of MAPLE software, covering the numerical solution of the equations and the geometric theory (drawing of the phase portrait and study of bifurcations).With the proposed study, it is intended to provide conditions for the student, who has already shown great potential for mathematical research, to improve and deepen her mathematical knowledge, particularly in the area of Ordinary Differential Equations. Moreover, the development of this project will provide the scholarship holder with an introduction to the development of mathematical research, maturing in the treatment of scientific literature, and preparing her for the development of more advanced research, with possible entry into a master's program and, in the future, into a doctoral program.